Download WIND EFFECT ON WATER SURFACE OF WATER RESERVOIRS

ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS
Volume LXI
203
Number 6, 2013
http://dx.doi.org/10.11118/actaun201361061823
WIND EFFECT ON WATER SURFACE
OF WATER RESERVOIRS
Petr Pelikán, Jana Marková
Received: December 12, 2012
Abstract
PELIKÁN PETR, MARKOVÁ JANA: Wind effect on water surface of water reservoirs. Acta Universitatis
Agriculturae et Silviculturae Mendelianae Brunensis, 2013, LXI, No. 6, pp. 1823–1828
The primary research of wind-water interactions was focused on coastal areas along the shores
of world oceans and seas because a basic understanding of coastal meteorology is an important
component in coastal and offshore design and planning. Over time the research showed the most
important meteorological consideration relates to the dominant role of winds in wave generation. The
rapid growth of building-up of dams in 20th century caused spreading of the water wave mechanics
research to the inland water bodies. The attention was paid to the influence of waterwork on its
vicinity, wave regime respectively, due to the shoreline deterioration, predominantly caused by wind
waves. Consequently the similar principles of water wave mechanics are considered in conditions
of water reservoirs. The paper deals with the fundamental factors associated with initial wind-water
interactions resulting in the wave origination and growth. The aim of the paper is thepresentation of
utilization of piece of knowledge from a part of sea hydrodynamics and new approach in its application
in the conditions of inland water bodies with respect to actual state of the art. The authors compared
foreign and national approach to the solved problems and worked out graphical interpretation and
overview of related wind-water interaction factors.
meteorology, water wave mechanics, wind-water interactions
The initial driving mechanisms for atmospheric
motions are related either directly or indirectly
to solar heating and the rotation of the earth.
Vertical motions are typically driven by instabilities
created by direct surface heating (e.g. air mass
thunderstorms and land-sea breeze circulations), by
advection of air into a region of different ambient air
density, by topographic effects, or by compensatory
motions related to mass conservation. Horizontal
motions tend to be driven by gradients in nearsurface air densities created by differential
heating and by compensatory motions related to
conservation of mass.
The waving on water reservoirs was investigated
by many scientists since the dams have started to be
built (e.g. Braslavskij, 1952; Saville, 1954; Kratochvil,
1970). They observed waves on inland water bodies
during various conditions and they published
the results which had the scientific impact into
these days in the region of Czech Republic and
Slovakia (Kálal, 1955; Kratochvil, 1970; Lukáč, 1972;
Marhoun, 1988; Šlezingr, 2004).
MATERIALS AND METHODS
Due to the complexity of the physical phenomena,
most methods for wave prediction are based on
semi-empirical relations. The methods have been
modified as wind and wave data were accumulated
over time, resulting in better predictions.
The energy transferred to the water level by wind
generates a range of wave heights and periods that
increase as the waves travel across the available fetch
length. Fetch means the area in which water level is
affected by wind having a fairly constant direction
and speed. The process of wave generation by wind
can be explained by combining the resonance
model developed by Phillips (1957) and the shear
flow model developed by Miles (1957). Pressure
fluctuations within the wind field disturb the still
water and cause water surface undulations. These
pressure fluctuations moving in the direction of the
wind resonate with the free wave speed and amplify
the undulations. As the size of these undulations
increases, they begin to affect the pressure
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Petr Pelikán, Jana Marková
distribution within the wind field, resulting in
a pressure difference between two wave crests. The
net force created by the higher pressure on the
windward face of the wave results in wave growth.
The important relationships between basic
magnitudes were analyzed in detail and their
graphical representation through charts was carried
out following the governing equations.
RESULTS AND DISCUSSION
Winds in coastal areas are influenced by a wide
range of factors operating at different space and time
scales. The important local effect in the coastal zone,
caused by the presence of land, is orographic effect.
Orographic effects are the deflection, channeling,
or blocking of air flow by land forms such as
mountains, cliffs, and high islands. A rule of thumb
for blocking of low-level air flow perpendicular to
a land barrier is given by the following ratio:
u < 0.1  blocked
 
hm > 0.1  no blocking
[-].
In the equation, u = wind speed and hm = height of
the land barrier in units consistent with u. Another
orographic effect called katabatic wind is caused by
gravitational flow of cold air off higher ground such
as a mountain pass. Since katabatic winds require
cold air they are more frequent and strongest in high
latitudes.
The estimation of winds from nearby
measurements has the appeal of simplicity and
has been shown to work well for large water bodies
(e.g. Great Lakes in USA). To use this method, it is
oen necessary to transfer the measurements to
different locations (from overland to overwater)
and different elevations (Ozeren, Wren, 2009). Such
complications necessitate provide some corrections
of wind speed.
The first correction refers to the measurement
location. The wind record from an anemometer
depends significantly on the physical conditions
of the surrounding terrain. The surrounding
terrain determines the boundary roughness and
thus the rate at which wind speed increases with
height above the ground. Consequently, physical
conditions characterizing the surrounding fetches
determine the wind environment at a site. At coastal
sites, the fetch oriented from beach over water is
generally characterized by relatively low roughness.
The fetch oriented from water to land can vary
significantly from site to site because it depends on
the type of vegetation, terrain, etc. Differences exist
between onshore and offshore wind speeds due
to differences in friction conditions over the fetch
(CERC, 1973). An empirical relationship between
overland wind speed (uland) and overwater wind
speed (uwater) can be estimated from measured wind
speeds at land and water sites by this formula (Hsu,
1981; Powell, 1982):
uwater = 1,62 + 1,17uland [-].
The authors of equation recommend to use the
formula when the air-water temperature difference
does not exceed 5 °C. The Fig. 1 shows the ratio
between overwater and overland wind speed as
a function of overland wind speed.
The Czech standard specification ČSN 75 0255
(Calculation of wave effects on waterworks) deals
with the estimation of overwater wind speed
differently. The standard specification introduce
the another term for fetch – effective length of wind
run over water. This approach has been used for the
determination of wave characteristics on valley dams
in the Czech Republic and Slovakia (Kratochvil,
1970; Lukáč, 1980; Šlezingr, 2004, 2007, 2010). Fig. 2
shows the relationship between the fetch length
and k-factor which is applied in the equation for
estimation of overwater velocity (ČSN 75 0255):
uwater = k × uland [-].
The second correction refers to the elevation of
wind speed. Oen winds taken from observations
do not coincide with the standard 10 m reference
level. They must be converted to the 10 m reference
level for predicting waves, currents, surges, and
other wind generated phenomena. Failure to do so
can produce extremely large errors. For the case
of wind in near-neutral conditions at a level near
the 10 m level (within the elevation range of about
1: Relationship between overwater and overland wind speed
Wind effect on water surface of water reservoirs
8–12 m), this simple approximation can be used
(uz = velocity at the desired elevation z, Fig. 3):
The net effect of wind speed variation with
fetch is to provide a smooth transition from the
(generally lower) wind speed over land to the
(generally higher) wind speed over water (U.S. Army
Corps of Engineers, 2002). The exact magnitude
and characteristics of this transition depend on
the roughness characteristics of the terrain and
vegetation and on the stability of the air flow.
Elevation and stability corrections of wind
speed provide a more comprehensive method to
accomplish the above transformation, including
both elevation and stability effects. The ratio of the
wind speed at any height to the wind speed at the
10 m height is given as a function of measurement
height for selected values of air-water temperature
difference and wind speed. Air-water temperature
difference (ΔT) is defined as:
ΔT = Ta − Tw [°C].
In the equation, Ta, Tw = air and water temperature
in °C. For air-water temperature differences
exceeding 5 °C, another correction can be applied.
A temperature correction applied to wind speed as
given by Resio and Vincent (1977) is:
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u’10 = RT × u10 [m.s−1].
In the equation, u’10 is the wind speed corrected
for the air-water temperature difference and RT is
the correction factor applied to the overwater wind
speed at the 10 m height (Fig. 4). The correction
factor RT is shown given by the equation:
RT = 1 ± 0,06878|Ta − Tw|0,3811 [-].
The physical processes that determine the
water surface wind field are contained in the basic
equations of motion. But, these equations are
mathematically very complex and can only be
solved by using numerical methods on high-speed,
large-scale computers. This approach is commonly
referred to as weather prediction by numerical
methods, pioneered originally by L. F. Richardson
(1922).
If one does not have access to a large computer
system with a real-time observational database, it
will be necessary to perform a manual analysis of
variables to construct the wind fields with the aid
of some simple dynamical relationships. Although
time consuming, manual analyses can produce
more detailed wind fields than models.
The basic force that drives waves is the surface
stress imparted by the wind however the parameter
2: K-factor for estimation of overwater velocity
3: Wind speeds (uz, u10) ratio due to elevation
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Petr Pelikán, Jana Marková
is not measured directly. It is estimated by knowing
the wind at a specified height (u10) and applying
an appropriate value for drag coefficient (Cd).
Determining Cd has been the objective of many field
research programmes over the years and there is one
of the result formulas:
Cd = 0,001(1,1 + 0,035u10) [-].
The drag coefficient is dependent on elevation and
stability (air minus water temperature difference) of
the atmosphere above the water level. In unstable
conditions the water is warmer than the overlying
air and there is more turbulent mixing in the lower
atmosphere. This increases the stress on the surface,
so for the same wind speed at a given height, waves
will become higher under unstable conditions
than under stable conditions (WMO, 1998). Hence,
characterizing friction and the stability in the lower
boundary layer is an important step in deriving
winds or surface stresses suitable for use in wave
estimation.
The boundary layer itself can be separated
into two regimes: the constant flux (or constant
stress) layer (from the surface to about 50 m) and
the Ekman layer (from about 50 m up to the free
atmosphere, approximately 1 km). In the surface
layer it can be assumed that the frictional forces
contributing to turbulence are constant with height.
The wind direction is consequently constant with
height. Using the mixing length theory developed
by Prandtl, it can be shown that the flow in the
constant flux layer (or Prandtl layer) depends only
on the surface roughness length (WMO, 1998).
Under neutral conditions, Prandtl’s solution
shows that the horizontal flow over the water
level follows the logarithmic profile in the vertical
direction:
uz 
u  z 
ln   [m.s−1].
  z0 
In the equation, κ is the von Kármán constant, z0 is
the constant of integration, known as the roughness
length, and u* is the friction velocity:
u  Cd u10 [m.s−1].
For subsequent wave forecast models, it appears
appropriate to express the input wind in terms of
friction velocity because this is calculated taking
stability into account. The wind is then expressed
at some nominal height by applying the neutral
logarithmic profile. This wind is then called the
equivalent neutral wind at that height.
Wind stress () considered as the rate of
momentum transfer into a water column (of unit
surface area) from the atmosphere can be written in
the parametric form, expressed as the relationship
4: Correction factor RT expressed as function of air-water temperature
difference
5: Increasing of the rate of momentum transfer with the wind velocity
Wind effect on water surface of water reservoirs
between drag coefficient, wind speed and air density
(a):
 = a × Cd × u2 [Pa].
Fig. 5 illustrates the relationship between wind
speed and wind stress.
CONCLUSION
Although wave generation by wind is complex, it
is possible to predict wave properties from the wind
data at a steady-state when speed and direction data
are available. Even though these data may not be
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available at a given field site, long-term estimates of
wave characteristics should be valid if theprediction
is based on wind data from the same region, as long
as the topography near the weather station is similar
to that of the water reservoir.
Knowledge of the wind characteristics, waves
and the forces they generate is essential for the
design of coastal projects because they are the major
factor that determines the geometry of beaches, the
planning and design shore protection measures and
hydraulic structures. Estimates of wave conditions
form the basis of almost all coastal engineering
studies.
SUMMARY
Aim of this work is the insight into fundamental wind-water interactions resulting in the wave
origination and growth. Proper wind estimation should involve following procedures and corrections.
When estimating wind characteristics from nearby measurements the correction of measurement
location has to be involved due to the roughness difference between water surface and surrounding
terrain. Since wind speed varies with the elevation this one has to be converted into the 10 m reference
level. Further the air-water temperature difference influence the resulting wind velocity so the
stability effects have to be taken into account. The magnitude called drag coefficient is dependent on
elevation and stability. This coefficient is applied to determine implicitly the surface stress imparted
by the wind. Thus, the input wind is expressed in terms of friction velocity because this is calculated
with respect to the stability effects.
The paper presents the utilization of piece of knowledge from a part of sea hydrodynamics and new
approach in its application in the conditions of inland water bodies with respect to actual state of the
art. The authors compared foreign and national approach to the solved problems and worked out
graphical interpretation and overview of related wind-water interaction factors.
The results contain graphical representation of some important relationships between discussed
magnitudes. Further, the results are applicable for more accurately establishment of wave heights on
water reservoirs due to wind with consequential better design of stabilization elements of dam and
water body shorelines.
Presented relationships among some basic processes in the energy transfer between wind and water
surface can facilitate insight into the wind-water interactions. Since the resulting wave prediction is as
accurate as the wind estimation is correct.
REFERENCES
BRASLAVSKIJ, A. P., 1952: Rasčet větrových voln.
Trudy GGJ, sv. 35/89, Leningrad: Gidrometeoizdat.
CERC, 1973, 1977, 1984: Shore Protection Manual.
Waterways Experiment Station, U.S. Army Corps
of Engineers, Washington, D.C.
HSU, S. A., 1988: Coastal Meteorology. New York:
Academic Press.
KÁLAL, I., 1955: Rozměry větrových vln na jezerech
a nádržích. Praha: Vodní hospodářství, 5.
KRATOCHVIL, S., 1970: Stanovení parametrů
větrových vln gravitačních vln v hlubokých
přehradních nádržích a jezerech. Vodohospodársky
časopis, 18, 3. ISSN 0042-790X.
LUKÁČ, M., 1972: Vlnenie na nádrži a jeho účinky na brehy
nádrže. Bratislava: MS Katedra Geotechniky SVŠT.
LUKÁČ, M., ABAFFY, D., 1980: Vlnenie na nádržiach,
jeho účinky a protiabrázne opatrenia. Bratislava:
Ministerstvo lesného a vodného hospodárstva SR,
108 s.
MARHOUN K., KUTÍLEK P., 1988: Ochrana břehů
nádrží proti abrazi. Brno: Hydroprojekt.
MILES, J. W., 1957: On the Generation of Surface
Waves by Shear Flows. Journal of Fluid Mechanics, 3:
185–204.
OZEREN, Y., WREN, D. G., 2009: Predicting Winddriven Waves in Small Reservoirs. American Society
of Agricultural and Biological Engineers, 52, 4: 1213–
1221. ISSN 0001-2351.
PHILLIPS, O. M., 1957: On the Generation of Waves
by a Turbulent Wind. Journal of Fluid Mechanics, 2, 5:
417–445. ISSN 0022-1120.
RESIO, D. T., VINCENT, C. L., 1977: Estimation of
Winds over the Great Lakes. J. Waterways Harbors
and Coastal Div., American Society of Civil Engineers,
102: 263–282. ISSN 0885-7024.
SAVILLE, T., 1954: The Effect of Fetch Width on
Wave Generation, Tech. Memorandum No. 70,
Beach Erosion Board, Corps of Engs.
ŠLEZINGR, M., 2004: Břehová abraze. Brno: 160 s.
ISBN 80-7204-342-0.
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ŠLEZINGR, M., 2007: Stabilisation of Reservoir
Banks Using an “Armoured Earth Structure”.
Journal of Hydrology and Hydromechanics, 55, 1: 64–
69. ISSN 0042-790X.
ŠLEZINGR, M., FOLTÝNOVÁ, L., ZELEŃÁKOVÁ,
M., 2010: Assessment of the Current Condition of
Riparian and Accompanying Stands. Colloquium
on Landscape Management 2010, Brno: Mendel
University in Brno, 24–27. ISBN 978-80-7375-6123.
U.S. Army Corps of Engineers, 2002–2011:
Coastal Engineering Manual 1110-2-1100, I–VI,
Washington D.C., p. 2923.
VOTRUBA, L., KRATOCHVIL, S., 1987: ČSN
75 0255 Výpočet účinků vln na stavby na vodních
nádržích a zdržích. Praha: Vydavatelství Úřadu pro
normalizaci a měření.
WMO, 1998: Guide to Wave Analysis and Forecasting.
2nd edition, WMO No. 702, Geneva: World
Meteorological Organization, p. 168, ISBN 92-6312702-6.
Address
Ing. Petr Pelikán, Ing. Jana Marková, Ph.D., Department of Landscape Management, Mendel University
in Brno, 613 00 Brno, Czech republic, e-mail: [email protected], [email protected]